Normally, for the plural, there is supposed to be an "r", here it there is not. Drengene is then an exception?
otherwise it should have been "Drengerne".
Is it for a purely phonetic reason or is there any rule about when not to put the "r"?
There are two was of forming the plural. One is with 'er' ones just an additional 'e'. But theres not really a rule when to use which. You just have to memorize it. So no its not an exeption, just one of two possibilities.
"Do the boys eat the meal?" is not correct in English, it makes no sense. Then on this page at the the top it says "Are the boys eating the meal?" which does. Why is this not consistent? correct answer needs to be more accurate on the quiz page.
The sentence: "Do the boys eat the meal?" sounds odd and a native English speaker would probably not say this. They would probably say "Are the boys eating the meal?" for present tense and "Did the boys eat the meal?" for past tense.